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Coordinate Plane/Transcript
Transcript Title text reads: The Mysteries of Life with Tim and Moby Tim and Moby are playing chess. Moby makes a move and checkmates Tim. TIM: How does a robot keep beating me? Moby smiles and hands Tim a letter. Dear Tim and Moby, How do you convert data from a table to a graph? Thanks, Taylor TIM: Well, to convert data to a graph from a table of values, like this one… you need to know about coordinate planes. On-screen, a table with 2 columns appears. The first column is labeled, x, value. The second column is labeled, y, value. Both columns are filled with numbers. TIM: A plane is a flat surface with length and width, but no depth. In other words, it has 2 dimensions, instead of 3. On-screen, a cube appears. It flattens into a square. A label reads, plane. TIM: And it has no edges; sort of like a piece of paper that goes on forever. On-screen, the plane expands and fills the screen. Moby beeps. TIM: Oh, well, planes aren’t real. They’re imaginary models of space. A coordinate plane is a plane overlaid with 2 perpendicular number lines. On-screen, an overhead view of the chessboard appears. The spaces on the board disappear and are replaced by 2 number lines, 1 vertical and 1 horizontal, which intersect at a point in the center. The horizontal line is labeled, x, axis. The vertical line is labeled, y, axis. TIM: Those lines help you find any point on the plane. It’s also known as a Cartesian plane, after René Descartes, the guy who developed the idea way back in 1637. On-screen, an image of René Descartes appears. A label reads, Cartesian plane. Another label reads, René Descartes. TIM: Basically, he drew 2 perpendicular lines in the middle of a plane and called the place where the lines intersect the origin. On-screen, the 2 lines of the plane appear. Moby's head appears where the lines intersect. A label reads, origin. TIM: 1 line represents the horizontal distance from the origin; we call that the x, axis. On-screen, Moby’s head slides back and forth on the horizontal x, axis. TIM: The other line represents vertical distance from the origin; that’s called the y, axis. On-screen, Moby’s head slides up and down on the vertical y, axis. TIM: These lines help us find our way around the plane. Moby beeps. TIM: Well, everything starts from the origin. The coordinates, or the address, of the origin are 0, comma 0. A label appears, reading, coordinates. Tim’s head appears at the plane’s origin, which is labeled, 0 comma 0. TIM: That means, to find the origin, you have to move 0 units horizontally and 0 units vertically. On-screen, Tim’s head tries to move away from the origin, but can’t. TIM: The set of numbers that describes a point is called an ordered pair, because the order of the numbers matters. A label appears, reading, ordered pair. A set of numbers in parentheses appears, reading, 2 comma 3. TIM: For instance, 2 comma 3, is different from 3 comma 2. Text appears, reading, 2 comma 3, does not equal 3 comma 2. TIM: The first number tells you the address of a point on the x, axis, while the second number tells you the address of a point on the y, axis. On-screen, the table appears. It shows that the ordered pair, 2 comma 3, has an x, value of 2, and a y, value of 3. TIM: So, to find the point described by the ordered pair, 2 comma 3, you’d start by looking at the first number, the x, coordinate. On-screen, the plane appears, with Tim’s head at the origin. The ordered pair, 2 comma three, appears, with the 2 highlighted. A label reads, x, coordinate. TIM: It tells you to go 2 units to the right. On-screen, Tim’s head slides 2 units to the right on the x, axis, landing on the number 2. TIM: Next, you look at the second number, the y, coordinate, which tells you to go 3 units up. A label appears, reading, y, coordinate. The 3 in the ordered pair, 2 comma 3, is highlighted. Tim's head slides up 3 units. TIM: Now I’m at the point, 2 comma 3. But if you were finding the point described by the ordered pair, 3 comma 2, you’d start out by going 3 units to the right and then 2 units up. Moby’s head appears at the origin and moves 3 units to the right, and 2 units up. The ordered pair, 3 comma 2, appears. Tim's head looks at Moby's head, which is located lower, and to the right. TIM: We’re in totally different places! Moby beeps. TIM: Each section of the coordinate plane is called a quadrant, cause there are 4 of them. A label appears, reading, quadrant. TIM: You can always predict what quadrant a point will fall in by looking at the positive and negative numbers. Quadrant 1 has all the points with a positive x, coordinate and a positive y, coordinate, like 2 comma 3. On-screen, the top right section of the plane is labeled, quadrant 1. The ordered pair, 2 comma 3, appears next to the point it describes. TIM: Quadrant 2 has all the points with a negative x, coordinate and a positive y, coordinate, like negative 2 comma 3. On-screen, the top left section of the plane is labeled, quadrant 2. The ordered pair, negative 2 comma 3, appears next to the point it describes. TIM: Quadrant 3 has all the points with a negative x, coordinate and a negative y, coordinate, like negative 2 comma negative 3. On-screen, the bottom left section of the plane is labeled, quadrant 3. The ordered pair, negative 2 comma negative 3, appears next to the point it describes. TIM: And quadrant 4… Moby beeps. TIM: Yep, quadrant 4 has all the points with a positive x, coordinate and a negative y, coordinate, like 2 comma negative 3. On-screen, the bottom right section of the plane is labeled, quadrant 4. The ordered pair, 2 comma negative 3, appears next to the point it describes. A dotted line connects all 4 points on the plane, forming a rectangle. Moby beeps. TIM: You can remember that x, comes first because, well, x, comes before y, in the alphabet. On-screen, Tim's head and Moby's head appear on the coordinate plane. Moby's head looks up at Tim's head and beeps. TIM: Nope, this doesn’t help me win chess at all. (sighs) Play again? Category:BrainPOP Transcripts